1. Field of the Invention
This invention relates to an optical waveguide device. This invention particularly relates to an optical waveguide device, which has an optical waveguide for guiding an optical wave therethrough and a grating coupler disposed on the surface of the optical waveguide such that the guided optical wave may be radiated by the grating coupler out of the optical waveguide, or such that an external optical wave may be introduced by the grating coupler into the optical waveguide.
2. Description of the Prior Art
Recently, a light deflector utilizing an optical waveguide has been proposed in, for example, Japanese Unexamined Patent Publication No. 62(1987)-77761 which corresponds to U.S. Pat. No. 4,778,991. The proposed light deflector comprises a slab-shaped optical waveguide, which is constituted of a material capable of propagating a surface acoustic wave therethrough, and a means for generating a surface acoustic wave in the optical waveguide such that the surface acoustic wave may travel in a direction that intersects an optical path of an optical wave guided by the optical waveguide. The frequency of the surface acoustic wave is changed continuously. By way of example, the means for generating a surface acoustic wave is constituted of an interdigital transducer and a driver for applying an alternating voltage, the frequency of which changes continuously, to the interdigital transducer.
With the aforesaid light deflector, the optical wave guided by the optical waveguide undergoes Bragg diffraction due to an acousto-optic interaction with the surface acoustic wave. The angle of diffraction changes in accordance with the frequency of the surface acoustic wave. Therefore, by varying the frequency of the surface acoustic wave in the manner described above, the optical wave can be deflected continuously in the optical waveguide.
Also, a novel light modulator has been proposed in, for example, Japanese Unexamined Patent Publication No. 1(1989)-178918 which corresponds to U.S. Pat. No. 4,961,632. With the proposed light modulator, the intensity of a surface acoustic wave, which travels through an optical waveguide, is modulated (or the surface acoustic wave is turned on and off), and Bragg diffraction of an optical wave guided by the optical waveguide is thereby controlled.
The optical wave, which has been deflected or modulated in the manner described above, can be radiated out of the optical waveguide by a grating coupler, a prism coupler, or the like, which is formed on the surface of the optical waveguide.
A recording medium may be scanned with an optical wave, which has been radiated out of the optical waveguide device constituted in the manner described above, and an image may thereby be recorded on the recording medium. In such cases, in order for a highly accurate image to be recorded, it is necessary that the scanning optical wave be converged into a small beam spot and the beam spot has a Gaussian intensity distribution at least with respect to a sub-scanning direction.
Also, in order for an optical wave utilization efficiency to be kept high, it is necessary that a guided optical wave be radiated out of an optical waveguide as efficiently as possible (e.g. at an efficiency of approximately 100%).
However, in cases where a guided optical wave is radiated out of an optical waveguide by using a grating coupler, it is very difficult for a beam spot having a Gaussian intensity distribution to be obtained. FIG. 5 is an explanatory view showing how the intensity of an optical wave, which has been radiated out of a grating coupler of a conventional optical waveguide device, is distributed. In FIG. 5, a linear grating coupler 42, which has uniform bar height and pitch, is located on the surface of an optical waveguide 41 formed on a substrate 40, and a guided optical wave 43 is radiated out of the optical waveguide 41. In such cases, as indicated by curve g, the intensity of a radiated optical wave 43' decreases exponentially with respect to the direction along which the guided optical wave 43 travels.
The exponential decrease in the intensity of the radiated optical wave 43' will hereinbelow be described in more detail. It is known that loss of the amount of the guided optical wave 43, .DELTA.I, (output optical amount) for a small region .DELTA.x of the grating coupler is expressed as ##EQU2## where I(x) represents the amount of the guided optical wave 43, and .alpha. represents the radiation loss coefficient. The radiation loss coefficient .alpha. is expressed as EQU .alpha.=ah.sup.m ( 2)
where h represents the heights of bars (or the depths of grooves) of the grating coupler, and a represents a coefficient. Solving the differential equation of Formula (1) under the boundary conditions of I(x)=Io for x=0 yields EQU I(x)=I.sub.o e.sup.-2.alpha.x ( 3)
From Formula (3), the entire amount of the radiated optical wave per unit length is expressed as ##EQU3##
In general, in the cases of rectangular gratings, the optical wave, which has been radiated out of a rectangular grating, is not constituted of a single wave, but multiple beam coupling is effected. Also, in the cases of weak coupling (i.e. when the radiation loss coefficient .alpha. is small), the ratio, P, of a radiated optical wave, which is to be utilized, to the entire radiated optical wave is constant. The intensity, J(x), of the optical wave to be utilized, which is radiated from a certain position x, is expressed as ##EQU4## Substitution of J(x) into Formula (4) yields EQU J(x)=2.alpha.PI.sub.o e.sup.-2.alpha.x ( 5)
For a grating coupler having uniform bar height, the value of h is constant, and substitution of Formula (2) into Formula (5) yields EQU J(x)=2P.multidot.(ah.sup.m)e.sup.-2ah.spsp.m.sbsp.x
Therefore, it can be known that the optical wave, which has been radiated out of a grating coupler having uniform bar height, has an exponentially decreasing intensity distribution.
In cases where a guided optical wave is to travel in the optical waveguide as shown in FIG. 5 and is deflected with a surface acoustic wave, the direction of the deflection (i.e. the main scanning direction) intersects the plane of the sheet of FIG. 5, and the sub-scanning direction is indicated by the arrow v. Specifically, the radiated optical wave 43' has an intensity distribution such that the intensity may decrease or increase exponentially with respect to the sub-scanning direction. Therefore, it is very difficult for a beam spot to be obtained which has a Gaussian intensity distribution with respect to the sub-scanning direction.
The aforesaid problem occurs when a guided optical wave is radiated by a grating coupler out of an optical waveguide. In cases where an external optical wave is introduced into the optical waveguide by using the grating coupler, the problem occurs in that the incident coupling efficiency cannot be kept high. Specifically, as can be understood from the reciprocity theorem regarding radiation and incidence of an optical wave, unless the incident optical wave has the intensity distribution indicated by curve g in FIG. 5, an optical wave cannot be introduced into the optical waveguide at a high efficiency as a whole. However, in general, optical waves produced by light sources, such as laser beam sources, have Gaussian intensity distributions with respect to the directions of diameters of optical wave beams. It is very difficult for such optical waves to be shaped into beams having an intensity distribution such that the intensity decreases or increases exponentially.
A novel grating coupler for solving the aforesaid problems has been proposed in Japanese Unexamined Patent Publication No. 61(1986)-286807. The proposed grating coupler is provided with bars having depths which are increased gradually in the direction along which a guided optical wave travels. However, this publication does not indicate anything about how the rate of change of the bar depths should be set for obtaining an approximately Gaussian radiated beam from the grating coupler and radiating a guided optical wave out of the grating coupler at a high efficiency (e.g. approximately 100%).
A different novel grating coupler for solving the aforesaid problems has been proposed in Japanese Unexamined Patent Publication No. 1(1989)-107213. The proposed grating coupler is provided with bars having heights which vary in a mountain pattern in the direction along which a guided optical wave travels. This publication indicates in detail how the heights of the bars of the grating coupler should be varied for obtaining an approximately Gaussian radiated beam from the grating coupler. However, the grating coupler provided with the bars having heights which vary in a mountain pattern is very difficult to fabricate.
Also, Japanese Unexamined Patent Publication No. 1(1989)-107213 does not indicate anything about how the heights of the bars of the grating coupler should be varied for radiating a guided optical wave out of the grating coupler at a high efficiency.
In Japanese Unexamined Patent Publication No. 4(1992)-40404, an optical waveguide device is disclosed wherein the heights of bars of a grating coupler are defined strictly such that the problems described above can be solved. Though the problems described above can be solved with the disclosed optical waveguide device, it has the drawbacks in that it is effective only when m=2 in Formula (2). It has heretofore been considered that the radiation loss coefficient .alpha. will be expressed as .alpha.=ah.sup.2. However, according to research carried out recently, it was confirmed that the radiation loss coefficient .alpha. may often be expressed as .alpha.=ah.sup.m, wherein 2&lt;m, depending upon the structure of the optical waveguide, or the like.